D&D 5E Level = Challenge Rating

[Yaarel]

They did the math, and it was bad math, but at least they showed their work.
Where is yours?

There are aspects of CR that work well. Mordenkainen (hence the 2024 monster math) made the 2014 Monster Manual math tighter, rather than introduce different math. The hit point bloat of monsters is intentional, altho slightly trimmer and more consistent in 2024. After a decade of play, something is passing the test of time − even if what this is is approximations generally, arbitrary and inconsistent.

Actually, 2014 CR never showed the work for its math. The 2014 Monster Manual ignores the math in the DMs Guide. Whatever "in house" formulas WotC designers are using remains unpublished. The designers say they often decide arbitrarily what the CR should be when the formula feels off.


With regard to "my math". The math of player character levels is already done, officially, in extreme detail, with ongoing corrections for balance and consistency.

The challenge here is to establish a formula to convert CR into levels, reliably. Once the levels come online for monsters, extreme precision and balance becomes possible.

 

[Yaarel]

The following is roughly true for Challenge ratings on average. It should probably be true for player character Levels as well. The Proficiency bonus is the same for both Challenge and Level. Meanwhile, it probably makes sense for player characters to acquire the very high Ability bonuses sooner (Strength, Intelligence, etcetera).

Level	Proficiency	Highest Ability	Attack = Proficiency + Ability
0	+1	+3	+4
1	+2		+5
2
3
4		+4	+6
5	+3		+7
6
7
8		+5	+8
9	+4		+9
10
11
12		+6	+10
13	+5		+11
14
15
16		+7	+12
17	+6		+13
18
19
20		+8	+14
21	+7		+15
22
23
24		+9	+16
25	+8		+17
26
27
28		+10	+18
29	+9		+19
30
31
32		+11	+20
33	+10		+21
34
35
36		+12	+22
37	+11		+23
38
39
40		+13	+24

Notice, if true for players: a character who uses the feats for Ability improvements, will be able to attain +5 at level 8, +6 at level 12, +7 at level 16, then entering Epic levels with +9. Most characters would spend their feats for other features, but these superhuman Abilities would become possible.

Superhero Abilities make sense anyway for levels 9-12, 13-16, and 17-20. Since most players today dont reach these tiers anyway, there will be negligible impact. Indeed to emphasize that these tiers are for the superhero genre can entice players to advance onward into these tiers.


Notice where Level 0 might have +3 as the highest Ability. This suggests that the "average" Human is +1. Then below average is +0, and above average is +2. Most Humans will be +1, with at least one Ability at +0, and +2 at one Ability that the individual tends to be good at. There can be outliers, such as +3 for a rare high Ability, or a negative bonus as a rare difficulty.


The monster Attack bonuses add together Proficiency and Ability. Very high Abilities become available sooner than expected relative to the Proficiency. The monsters rarely include magic items as part of this Attack bonus. But the very high number sometimes implies magic. For example, an Attack bonus of +11 at Challenge Level 13, might represent the +5 Proficiency, then only a +4 Ability and by implication a +2 weapon. Every monster statblock is its own concept, but the Proficiency is always true, and it is the Ability and magic that depend on concept.


The high Attack bonuses correlate very high Ability bonuses that can boost AC as well. These big numbers deviate from the goal of "bounded accuracy". Once modifications are adding +11 to a d20, creatures are becoming unreachable by lower tier creatures.

I am ok with the defacto slackening of bounded accuracy that has already happened. It still is at a slower pace than 3e. At the same time, each four-level tier feels different from the tiers before and after. Each tier is a different league of play. At level 9 with its tier 9 thru 12, the superhero genre is starting to happen with figures like Batman and Legolas. Meanwhile the standard superhero is tier 13 thru 16 and should feel different again. The most powerful superheroes like Storm and Superman are different yet again at the tier of 17 thru 20. The Epic levels truly feel beyond.

D&D 5e has already evolved its bounded accuracy this way. It is what it is. The big numbers exist. But I also think, these 5e numbers are optimally where they should be.

By extension, a player character should be able to use the feat at level 12 to boost an Ability to +6.

 

[Yaarel]

Damage-Per-Round for both monster Challenge and player Level is about the same.

In this context, the DPR assumes the players are unloading all available resources, such as any top spell slots. It makes sense that monsters are also unloading all available resources during the three or so rounds of the combat encounter.

Single-target spells work out to be about 4.5 damage per player Level. This compares well for monster damage at about 5 damage per Challenge.


Note, player "baseline" DPR tends to be about 6 damage at Level 1 and eventually 35 damage at Level 20. Hence: (L+3)*1.5.

At Level 20, the DPR can range from about 25 to 45 depending on the build.

It is a player character going nova that compares to a monster.

 

[Yaarel]

With regard to building a standard combat encounter.

Three player characters combat one monster whose Challenge is about the same number as the Level of the player characters.

One player character combats one monster whose Challenge is about a third of the Level of the player character.


As a rule of thumb, tho there may be other factors that introduce distortions:

Challenge = (Level/3) * number of player characters

Spoiler: Comparison

CHALLENGE OF MONSTER

Four Heroes Per Monster (Sly Flourish)	≈ L * 4/3	Three Heroes Per Monster	≈ LEVEL	Two Heroes Per Monster (Sly Flourish)	≈ L * 2/3	One Hero Per Monster (DMs Guide)	≈ L * 1/3	Two Monsters Per Hero (Sly Flourish)	≈ L * 1/6	Three Monsters Per Hero	≈ L * 1/9	Four Monsters Per Hero (Sly Flourish)	≈ L * 1/12
1	1.333		1	½	0.6667	¼	0.3333	−	0.1667		0.1111	−	0.08333
3	3		2	1	1.3333	½	0.6667	−	0.3333		0.2222	−	0.1667
4	4		3	2	2	1	1	¼	0.5		0.3333	−	0.25
5	5		4	2	3	1	1.333	¼	0.6667		0.4444	−	0.3333
8	7		5	4	3	2	1.667	1	0.8333		0.5556	¼	0.4167
9	8		6	5	4	3	2	1	1		0.6667	¼	0.5
10	9		7	6	5	3	2	1	1.167		0.7778	½	0.5833
12	11		8	6	5	3	3	1	1.333		0.8889	½	0.6667
12	12		9	7	6	4	3	2	1.5		1	½	0.75
14	13		10	7	7	4	3	2	1.667		1.111	½	0.8333
15	15		11	8	7	5	4	3	1.833		1.222	1	0.9167
17	16		12	10	8	5	4	3	2		1.333	1	1
18	17		13	10	9	6	4	3	2		1.444	1	1.083
19	19		14	11	9	6	5	4	2		1.556	1	1.167
20	20		15	12	10	7	5	4	3		1.667	1	1.25
20	21		16	13	11	7	5	4	3		1.778	2	1.333
21	23		17	14	11	8	6	4	3		1.889	2	1.417
21	24		18	14	12	8	6	5	3		2	2	1.5
22	25		19	15	13	9	6	5	3		2	2	1.583
23	27		20	16	13	10	7	6	3		2	3	1.667